Sewer design slide rule



I. GOLDFIEN SEWER DESIGN SLIDE RULE Nov. `162 1948.

2 sheets-sheet 1 Filed Feb. 21, 1948 i3] /NVENTOR /Rv/NG GOLD/:15N M70/m@ ATTORNEY 1. GoLbFn-:N 2,454,157

SEWER DESIGN SLIDE RULE '2 Sheets-Sheet 2 Nov. 16, 1948.A

Fired Feb. 21. 1948 Patented Nov. 16, 1,9418l UNITED STATES PATENT OFFICE SEWER DESIGN SLIDE RULE Irving Goldfen, Milwaukee, Wis.

Application February 21, 1948, Serial No. 10,129

Claims.

The present invention relates to slide rules and more particularly to those for solving problems in sewer design.

The Chezy formula, V=C\/RS, for water flow in pipes and channels, is known as the Kutter formula when for C is substituted an expression depending on the roughness of the channel, the slope S -and the hydraulic radius R, i. e., the crosssectional area divided by the wetted perimeter. The usual Kutter expression for C, in English measure, is

in which N is the Kutter coeiilcient of roughness or friction, this coeiiicient or factor increasing with roughness. The values of N used in sewer design ordinarily range from .011 to .015, although lower and higher values are occasionally encountered.

The elements or factors involved in th'e design of circular sewers are: Q, the quantity of flow in cubic feet per second; N, the friction factor; D, the diameter of the sewer pipe in inches; L, the length of the pipe in feet; H, the drop of the pipe in feet; Parts Full, the relative depth of now in the pipe; V, the velocity of flow in feet per second; and T, the time of flow in minutes. When any five of these eight elements are known, the values of the other three elements can be determined.

An object of the invention is to provide an improved and simply operated sewer design slide rule based on the Kutter formula and arranged for quickly and accurately solving a wide variety of problems involving circular sewers.

Another object is to provide a sewer design slide rule which includes accurate and easily readable scales of wide range while being of a handy size, a typical length of the new rule being about 13 inches which permits the device to be conveniently carried in a pocket or brief case for iield use,

The invention further consists in the sever-al features hereinafter described and claimed.

In the accompanying drawings,

Fig, l is a plan view showing the front face of a slide rule constructed and arranged in accordance with the invention, parts being broken away;

Fig. 2 is a plan view showing the rear face of the slide rule, parts b-eing broken away;

Fig. 3 is an enlarged plan View showing the middle portion of th'e front face of the rule, parts 2 being broken away anda slide member of the rule being shifted to the right, and

Fig. 4 is a transverse sectional view of the slide rule, taken on the line 4-4 of Fig. 3.

In the drawings, the numerals IU and II respectively designate rectangular front and rear frame plates which are separated by longitudinal marginal strips I2, the plates and strips being secured together as by countersunk tubular rivets I3. The frame assembly or body thus formed presents a longitudinal slot or passage I4 receiving and guiding therein a plate-like slide I5, the ends of the frame plates having notches I6 to facilitate longitudinal displacement of the slide. The front frame plate ID has elongated rectangular upper and lower windows I'I and I8, respectively, and the rear frame plate II h'as an elongated rectangular window I9, all the windows extending parallel to the upper and lower edges of the frame plates. A runner 20 slidably embraces the frame assembly, and by way of example may be formed of a transparent sheet of plastic material, such as cellulose acetate, having thereon a front hairline 2I and a rear hairline 22 each extending at right angles to the windows.

The front of the slide rule is divided into upper and lower rule sections or halves, hereinafter described, by a heavy horizontal line 23 on the front frame plate, the windows I'I and I8 being respectively disposed in these sections.

The front frame plate has printed or engraved thereon above and along the upper window, I'I, a logarithmic quantity scale Q and a logarithmic velocity scale V, the Q scale (designated cu. ft. per sec. .8 full) being in cubic feet per second and ranging from .25 to 2000 cubic feet, left to right, Iand the V scale (designated ve1. ft. per sec. .8 full) being in feet per second and ranging from 1 to 1G() feet, left to right. Each member on the V scale coincides with a number ten times as large as the Q scale. If desired, these scales may be printed in contrasting colors.

Below and along the upper window, I'I, the front frame plate has several parallel scales D1, D2, and D3 of circular pipe sizes, designated diam. in inches, for diierent Kutter N coeiilcients, here sh'own for N=.0l5, N=.013, and N=.011, the pipe sizes ranging from 8 to 216 inches in diameter and increasing from left to right. The N coefficients given are those most commonly used, being for brick, concrete and vitried clay sewer pipes; however, additional or substitute D scales may be provided for larger or smaller N coeiiicients. For extremely smooth pipes, such as those of asbestos-cement, the value of N ranges from .009 to .011, while for corru gated steel pipes the value of N ranges from .015 to .021. Each of the D scales has additional indices for pipes of 6 inch and 8 inch diameter, these indices being the encircled numbers 6 and 8 and being so located as to permit computations for pipes of 6 inch diameter without extending the length of the slide rule. These computations will involve multiplication or division by 10 of the given or found Q values. The D scales are offset to the left with increasing value of N. By way oi example, a i8 inch pipe on the scale N=.(l15, corresponds approximately to a 45 inch pipe on the scale N=.O13 and a l2 inch pipe on the scale N:.011.

Along its upper1 portion the slide has several scales visible through the window il and associated with the adjacent scales on the front plate to form the upper rule section. These slide scales consist of a length scale L, a drop scale H therebelow, and a parts full scale at the left of the L scale. The L scale. which is for the length of the sewer in feet, ranges from 300() to 10, left to right; the H scale, which is for the drop of the sewer in feet, ranges from 40 to .01, left to right; and the parts full scale ranges from .1 to 1, left to right. The parts full scale and the L scale extend along the 'upper edge of the window ill, and the H scale extends along the lower edge of this window. The scales of the upper rule section are adjusted for the sewer running .8 full, a point when the velocity is practically the greatest and the discharge about 98% of the discharge running full. The parts full scale is provided for converting the discharge for other depths of iiow on the upper scales. It will be noted that in the parts iull scale the number 1.0 is placed between .8 and .9 and is close to .8. This relation reilects the fact that in a circular pipe the dow running .8 full is nearly as large as the flow running full, and that the maxim-urn iiow occurs with the pipe running about 93% full. A margin of carrying capacity is thus provided.

Above and along the lower window, E3, the front plate has a logarithmic time scale T, designated minutes .8 full, ranging from l to .1, left to right, and being based on a pipe flowing .8 full. Below and along the window i6 the front frame plate has several parallel scales D4, D5, De, of circular pipe sizes, for diiierent Kutter N coeilicients, arranged in the same general manner and for the same values of N as the D scales of the upper rule section, but being somewhat reduced. Each lower D scale begins at the left with a Value for a pipe of 6 inch diameter.

Along its lower portion the slide has several scales visible through the window i3 and associated with the adjacent scales on the iront plate to form the lower rule section. These slide scales consist of a length scale L, a drop scale H therebelow and a parts full scale at the left of the H scale. The lower H scale is identical with'the upper H scale, and the lower L scale is similar to the upper L scale except that the former is somewhat enlarged and extends from 3000 to 20, left to right. Both L scales and both H scales are logarithmic. The low values on both of the L scales permit computations involving relatively short sewers, such as transverse sewers connecting parallel sewers laid in wide streets. The scales of the lower rule section are adjusted for a sewer running .8 full, like the scales of the upper rule section. In the lower parts full scale the .member 1 is over the member .5, reflecting the fact that the hydraulic radius is the same for both depths of flow. Also, the number .9 is placed between the terminal number .8 and the number .7, reflecting the characteristics of the flow. The hairline 22 of the runner cooperates with the various scales of the upper and lower sections. The upper and lower rule sections are so related as to permit the conjoint use thereof, in association with the runner, for solving various problems insewerdesign. .Certaintypes or" problems can also be solved by using either rule section alone. The rear frame plate has printed theree on instructions Zhi for the use of the slide rule, these instructions being in the form oi" typical sewer` design problems and their solution.

The rear face of the slide rule is also provided with standard engineers slide rule scales A, B, CI, C, D, and K for general computation, the rear frame plate being provided with the scales A, D, and K extending along the window i9, and the slide being provided with .the .scales B, CI, and C. The hairline 22 of therunner cooperates with these scales.

The general use of the slide rule is asfollows: Assume .that cubic feet of sewage per second is to be discharged through a sewer'OOieet long, whose coefficient of friction is .013. 1f "50,0 on .the upper L scale is set under the quantity 100 on the Q scale, the drops required for varioussizes oi sewers may be read on the upper H scale over the divisions on scale D2 corresponding ,to .the pipe diameters for N=.0i3. For a coefficient of friction 1\l=.015, the rule would be set in the same manner, but the required drop Iwould. be read on the upper -H scale over the divisions on scale Di corresponding to the pipe diameters for N=.()15. The drop for other coeiicients may be obtained by visual interpolation between the corresponding scale divisions of adjacent lD scales, and even by extrapolation. For certain types of problems the points of interpolation may be jprojected to other scales of the rule by hairline 2l of the runner,

Ii the time of running in an established sewer is desired, the procedure is as follows: The drop on the lower H scale is set over the divisioncorresponding to the pipe size on the lower D scale for the assumed coeiiicient of friction. .The time of running in minutes may then be read on the T scale over the sewer length on the lower L scale. With the same setting the velocity of'fiow may be read on the V scale over Vthe length on the upper L scale.

The use of the slide rule in sewer design is illusl trated by the following examples:

EXAMPLE 1 A sewer is to Ibe 500 it. long and yis to discharge 14 cu. ft. per sec. The maximum amount of available fall is 2.3 ft.

(o) What is the necessary size and fall .of the sewer if it is to run .8 full, assuming N:.013?

(b) What would be lthe velocity and time of i'low? Solution (a) Using upper half or" rule set 500 on L under 14. on Cu. Ft. per Sec. The drop 2.3 ft. on H comes between 21 and 24 on the line N=.0l3. Therefore diameter of sewer would-be 24 and the required drop is `read on `the H scale over 24., or 1.97 it.

(t) Using the lowerh-alf of rule set 1.97;ft.-on.H over 24.- on line N=.013; then over l500 on upper L nd velocity Ito be 5.28 it. per s.ec.;:.and vover:50.0

on lower L find time of flow to be 1.57 minutes on T scale.

EXAMPLE 2 (Using the data in Example 1) (a) What is the necessary size and fall of the sewer if it is to run full? (b) What would be the velocity and time of iiow? Solution (a) Using upper half of rule set 1.0 on Parts Full under 14. on Cu. Ft. per Sec. Over .8 on Parts Full iind 13.70 cu. ft. per sec. the discharge when flowing .8 full. Now set 500 on L under 13.70 on Cu. Ft. per Sec., and by using runner read off the rst size on line N=.013 bevond the division 2.30 on H, which gives a 24 sewer anda drop of 1.90 ft.

(b) Using the lower half of the rule set .8 on Parts Full over 24 `on line N=.013; with slide in this position, move runner to 1.0 on Parts Full, and then move slide to lbring 1.90 on H under hairline of runner. Then over 500 on upper L find velocity=4A7 It. per sec.; and over 500 on lower L nd time of ow to be 1.86 minutes.

EXAMPLE 3 A sewer is to be 500 ft. long and i-s to discharge 14. cu. ft. per sec. The maximum amount of available fall `is 2.90 ft.

(a) What is the necessary sizeof the sewer and the Parts Full of the sewer if the actual fall to be used is 2.90 ft. assuming N=.013?

(b) What would be the velocity and time of flow? Solution As in Example 2, nd size of sewer to be 24 land necessary drop to be 1.90 ft.

(a) Using upper half of rule, set runner hairline on 24 on line N=.013; set 2.90 on H under hairline. Move hairline to 500 on L. Set .8 Parts Full" under hairline. Move hairline .to 14. on Cu. Ft. per Sec. Read .68 Parts Full under hairline.

(b) Using lower half of rule, set hairline on 24 on line N=.013; set .8 Parts Full under hairline. Move hairline to .68 Parts Full. Move slide so that 2.90 on H is under hairline. Then over 500 on upper L iind velocity to be 6.17 ft. per sec., and over 500 on lower L find time of ow to be 1.35 minutes.

EXAMPLE 4 A 12" sewer is to be 100 it. long :and to have a drop of 1.00 ft.

(a) What is the discharge if it is to run full, assuming N=0.15?

(b) What would he the velocity and time of flow? Solution (a) Using upper half of rule, set runner hairline over 12" on line N=.015. Set 1.00 on H under hairline, and over 100 on L read 2.80 on Q. Move hairline to 2.80 on Q `and set .8 on Parts Ful under hairline. Then move hairline lto 1.0 on Parts Full and read the discharge, 2.86 cu. ft. per sec., `on Q.

(b) Using lower half of rule, set .8 Ion Parts Full over 12H on line N=.015. With slide in this position, move hairline to 1.0 on Parts Full, and then move slide to bring 1.00 on H under hairline of runner. Then over 100 on upper L nd velocity to be 3.60 it. per sec. on V; and `over 100 on lower L find time of 110W yto be 0.465 minute on T.

EXAMPLE 5 An 8" sewer is to be 100 ft. long, flowing .5 full, with a velocity of 2.70 it. per sec.

(a) What is the discharge in cu. ft. per sec. and the required drop in ft., Iassuming N=.015?

(b) What is the time of flow? Solution (a) Using lower half of rule, set runner hairline over 8" yon line N=.015 :and set .8 on Parts Full under hairline. Move hairline to .5 on Parts Full, and with runner in this position move slide so that on upper L is under 2.70 on V. The required drop is read on lower H under the hairline as 1.10 it. Over 100 on lower L, the time of ilow is read on T as 0.617 minute.

(b) Using upper half lof rule, set hairline over S on line N=.0l5. Set 1.10 on H under hairline Iand over 100 on L read 0.94 cu. ft. per sec. on Q for .8 full. Set hairline on 0.94 on Q, set .8 on Parts Full under hairline and move hairline to 0.5 on Part-s Full. Then on Q read 0.48 cu. ft. per sec.

EXAMPLE 6 A 30" sewer is to be 100 ft. long.

(a) What is the discharge if it is to run full, assuming N=.01l?

(b) What is the necessary drop and velocity if the time of flow is 0.29 minute? Solution (a) Using lower half of rule, set hairline over 30 on line N=.011. Set .8 on Parts Full under hairline and move hairline to 1.0 on Parts Full. With hairline in this position set 100 on L under 0.29 minute on T. Then on H' read a drop of .31 ft., and over 100 on upper L read 5.75 ft. per sec. on V.

(b) Using upper half of rule, set hairline over 30 on line N=.011. Set 0.31 on H under hairline, and over 100 on L read 27.7 cu. it. per sec. on Q for .8 fall. Move hairline to this discharge, and set .8 on Parts Full under hairline; move hairline to 1.0 on Parts Full, and read on Q the required discharge of 28.30 cu. ft. per sec.

EXAMPLE 7 A 30 sewer has a length of 100 ft, and a drop .04 feet, and flows full at a velocity of 2.05 it.

per sec.

(a) What is the discharge and the value of the friction factor N? (b) What is the time of flow? Solution (a) Using upper half of rule, set 100 on L under 2.05 on V, and on lower half of rule read 0.81 minute on T over 100 on L. With this setting move hairline to a drop oi .04 on lower H. Set 1.0 on lower Parts Full under hairline; then move hairline to .8 on Parts Full, and under hairline read 30 diameter on line N=.011.

(b) Using upper half of rule set hairline over 30" on line N=.011; set .04 on H under hairline, and over 100 on L read 10.00 cu. ft. per sec. on Q. Move hairline to 10.00 on Q and set .8 on Parts Full under hairline; then move hairline to 1.0 on Parts Full, and on Q read the required discharge, 10.20 cu. ft. per sec.

EXAMPLE 8 An 18" sewer 100 ft. long, with a drop of 1.00 foot, discharges 0.93 cu. ft. per sec.

(a) What is the relative depth of ow? (b) What is the velocity and time of iiow? aisgisvf Solution (a) Using upper half of rule, set hairline over 18 on line N=.01S; under hairline set 1.0 on H, and over 100 on L read 10.10 cu. ft. per sec. on Q for .8 full. Set .8 on Parts Full under 10.10 on Q and move hairline to 0.93 cu. ft. per sec. on Q. Then on Parts Full and read 0.20 near hairline.

(la) Using lower half of rule, set hairline over i8 on line l\l`:,013. Set .8 on Parts Full under hairline, and then move hairline to 0.20 on Parts Full. Set drop of 1.00 on I-I under hairline. rThen over 100 on upper L read 3.30 ft. per sec. on V, and over 100 on lower L read 0.50 minute on T.

The foregoing examples are given to illustrate the solution oi typical sewer design problems, but othe' related problems with different given and required elements can also be solved.

In arranging the slide rule, the logarithmic quantity of ow scale, Q,v of the desired wide range of values, and the various N scales, for the desired wide range of pipe diameters, are laid out to extend over the available length of the rule. The quantity of flow is equal to the crosssectional area oi the water in the pipe (in this` case for a pipe owing .8 full) multiplied by the velocity oi ilow. The velocity scale, V, of the desired range, is of a convenient size to be superimposed on the quantity of ilow scale, Q. The upper L, H, and Parts Full scales, and the various scales of the lower rule section, are then adjusted in accordance with the requirements of the Kutter formula.

The arrangement of the slide rule enables extensive scales oi values to be provided in a rule of handy size and facilitates the solution of a wide variety of problems in the design of circular sewers.

What Iclaim as new and desire to secure by Letters Patent is:

l. A Kutter-formula sewer design slide rule for circular sewers, comprising a body member and a slide member movable with respect thereto; said rule having rst and second rule sections disposed one above the other; the irst rule section having on the body member a logarithmic quantity of ilow scale and a logarithmic velocity of flow scale each for sewers running .8 full, and a plurality of scales of sewer diameters for different Kutter coefficients-of friction; the second rule section having on the body member a logarithmic time of flow scale for sewers running .8 full and a plurality of scales of sewer diameters for different Kutter coeliicients of friction corresponding to those for the rst section; each of said rule sections having on the slide member a logarithmic sewer length scale, a logarithmic sewer drop scale and a Parts Full conversion scale.

2. A Kutterformula sewer design slide rule for circular sewers, comprising a pair of relatively slidable first and second members; said rule having first and second rule sections disposed one above the other; the irst rule section having on the ilrst member a logarithmic quantity'of iiow scale and a logarithmic velocity of flow scale each for sewers running a predetermined relative depth full and a plurality of scales of sewer diameters for diierent Kutter coeiicients of friction; the second rule section having on the irst member a logarithmic time of flow scale for sewers running the predetermined depth full and aplurality-ofscalesof sewer diameters for different Kutter coefcients of friction corresponding to'those for the irstrulesection, each of the rule sections having on the second member a logarithmic sewer length scale, a logarithmic sewer drop scale, anda Parts Full conversion scale.

3. AV Kutter-formula sewer design slide rule for circular sewers, comprising a pair of relatively slidable rst and second members; said rule havm ing first and second rule sections disposed one over theA other; the rst rule sectionA having on the iirst memberaY logarithmic quantity of ilow scale and a logarithmic velocity of `ow scale each for sewers ruiming a predetermined relative depth full and a scale of sewer diameters for a predetermined Kutter coefiicient of friction; the second rulesection having on the first member a logarithmic time of ilow scale for sewers run-v ning the predetermined depth full and a scaler of sewer diameters for the predeterminedI/utter coe eflicient of friction; each of the rule sections having on the second-member a logarithmic sewer length scale and a logarithmic sewer drop scale.

4. A' Kutter-formula sewer design slide rulefor circulary sewers, comprising a pair of', relatively slidable irst and second members together forming upper and lower rule sections; the upper portion of said'rst' member having a logarithmic quantityof flow scale and a logarithmic velocity of flow scale each for sewers running .8 full, and a plurality of scales of sewer diameters for diierent Kutter coeihcients of friction; the lower portion of said iirst. member having a logarithmic time or" ilow scale for sewers running .8 full and a plurality of scales of sewer diameters for diirerent Kutter coecients of friction corresponding to those for the rst rule section; said slide member having as elements of the upper andlower rule sections respective sets oi' scales comprising a logarithmic sewer length. scale, a logarithmic sewer. drop scale, and a Parts Full conversion.

scale.

5..A Kutter-formula sewer design slide rule forV circular sewers, comprising an elongated rule frame having a pair of parallel upper and lower windows, and a. slide carried by said frame and visible at said windows; said frame and slide forming upper and lower rule sections; said frame having along one of said windows a logarithmic Quantity of flow scale and a logarithmic velocity of ow scale each for sewers running .8 full, and a plurality of scales of sewer diameters for different Kutter coefficients of friction; said frame further having along the other window alogarithmic time or' ow scale and a plurality of scales of; sewer diameters for different Kutter coeili-l cients of friction corresponding to those for the diameter scales along the-first window; said slide having as elements for the upper and lower'rule sections respective sets of scales comprising a logarithmic sewer length scale, a logarithmic sewer dro-p scale, and a Parts Full conversion scale, one set of said scales along each window.

IRVING GOLDFIEN.

Name Date Spitzglass July 5, 1915 Number 

